A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time t is given by s = t2 + at - b + 17, where a and b are real numbers. If the particle comes to rest after 5 s at a distance of s = 25 units from the fixed point, then values of a and b are, respectively
10, - 33
- 10, - 33
- 8, 33
- 10, 33
If a, band c are in AP, then the straight line ax + 2by + c = 0 will always pass through a fixed point whose coordinates are
(1, - 1)
(- 1, 1)
(1, - 2)
(- 2, 1)
A.
(1, - 1)
Given that, a, band c are in AP
and equation of straight line is
ax + 2by + c = 0
On comparing, we get
x - 1 = 0
and 2y + 2 = 0
Hence, the required fixed point is (1, - 1).
Let P and Q be the points on the parabola y2 = 4x so that the line segment PQ subtends right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is
1
2
4
6
If the three points A(1, 6), B(3,- 4) and C(x, y) are collinear, then the equation satisfying by x and y is
5x + y - 11 = 0
5x + 13y + 5 = 0
5x - 13y + 5 = 0
13x - 5y + 5 = 0
In a right-angled triangle, the sides are a, b and c with c as hypotenuse and c - b 1, c + b 1. Then the value of (logc + b(a) + logc - b(a))/ (2logc + b(a) x logc - b(a)) will be
2
- 1
1
The equation , y = 1 are the sides
an equilateral triangle
a right angled triangle
a isosceles triangle
an obtuse angled triangle
If C is a point on the line segment joining A(- 3, 4) and B(2, 1) such that AC = 2BC, then the coordinate of C is
(2, 7)
(7, 2)